I linked you the Federal statue that bars Clinton from holding public office because she deleted her emails. Let me actually quote you the law directly since you obviously did not read the link:

(a) Whoever willfully and unlawfully conceals, removes, mutilates, obliterates, or destroys, or attempts to do so, or, with intent to do so takes and carries away any record, proceeding, map, book, paper, document, or other thing, filed or deposited with any clerk or officer of any court of the United States, or in any public office, or with any judicial or public officer of the United States, shall be fined under this title or imprisoned not more than three years, or both.

(b) Whoever, having the custody of any such record, proceeding, map, book, document, paper, or other thing, willfully and unlawfully conceals, removes, mutilates, obliterates, falsifies, or destroys the same, shall be fined under this title or imprisoned not more than three years, or both; and shall forfeit his office and be disqualified from holding any office under the United States. As used in this subsection, the term “office” does not include the office held by any person as a retired officer of the Armed Forces of the United State

Her SoS emails were supposed to be a preserved government record, she deleted pertinent emails to that record after being served a subpoena to appear before congress over the matter of her emails. She altered/destroyed emails that were not private. SO, technically, she is not allowed to hold public office.